The study, published in Frontiers in Antennas and Propagation by Hatice-Andreea Topal and Teodor Lucian Grigorie, is notable less for any single record-breaking number and more for its methodology. Rather than analyzing one antenna in one simulator, the team designed both structures analytically using classical horn theory implemented in Matlab, then validated each design in two independent electromagnetic environments, Ansys HFSS and CST Studio Suite. This cross-platform approach is a kind of computational sanity check that many antenna papers skip, and it paid off: the two simulators produced results in close agreement, with only minor differences attributable to their fundamentally different numerical engines.

The pyramidal horn, fed by a standard WR-90 rectangular waveguide with interior dimensions of 22.86 by 10.16 millimeters, was designed around a target gain of 22.70 decibels at a central frequency of 10 gigahertz. The aperture measures 178.5 by 145.8 millimeters, with an axial flare length of roughly 323 millimeters. In simulation, the antenna exceeded expectations, delivering a maximum gain of 23.63 decibels with an extraordinarily narrow half-power beamwidth of between 6 and 10 degrees. The reflection coefficient, a measure of how much signal bounces back toward the transmitter instead of radiating into space, dipped as low as minus 39.43 decibels at 8.22 gigahertz in HFSS and an impressive minus 56.18 decibels at 8.07 gigahertz in CST, both comfortably below the minus 10 decibel threshold that defines good impedance matching.

Those numbers matter because a well-matched antenna wastes almost none of the precious power an amplifier sends its way. The Smith chart analysis from the simulations showed the input impedance hugging the ideal 50-ohm target, landing near 50 plus or minus 3 ohms with negligible reactance, which corresponds to a voltage standing wave ratio of approximately 1.05. In practical terms, the pyramidal horn is a highly efficient, laser-focused energy projector, ideal for applications demanding pinpoint directivity and clean linear polarization.

The conical horn tells a different story. Fed by a BY89 circular waveguide 23.825 millimeters in diameter, with a dominant TE11 mode cutoff frequency of 8.67 gigahertz, the cone achieved a maximum gain of 16.43 decibels and a much wider beamwidth of about 30 degrees. Its reflection coefficient stayed below minus 10 decibels across the entire 9-to-12-gigahertz operating range, bottoming out at minus 43 decibels at 11.22 gigahertz in HFSS. That wider, symmetric beam is not a weakness; it is exactly what a reflector feed needs to illuminate a parabolic dish uniformly without spilling energy over the edges.

The real magic of the cone, however, is polarization. By exciting two orthogonal TE11 modes with equal amplitudes and a 90-degree phase difference through a bimodal wave port, the researchers generated circular polarization with an axial ratio below 3 decibels across the main lobe. This is a decisive advantage in satellite communications, where circularly polarized signals tolerate the orientation mismatch that inevitably arises between a moving spacecraft and a ground antenna. The conical design achieved circular polarization discrimination of 57 to 62 decibels on the principal axis, approaching the performance of the corrugated horns flown on operational satellites, yet without any corrugations or added polarizer hardware.

The comparative metrics sharpen the choice further. The conical horn posted an aperture efficiency of roughly 74 percent against about 64 percent for the pyramid, and its slightly higher radiation efficiency, about 96 percent versus 94 percent, follows from its smaller inner surface area and thus lower ohmic loss. Both exceed the 90 percent mark comfortably. In the satellite link budget, a 10 percent aperture efficiency improvement can translate into an additional half to one decibel of system gain, a meaningful margin when every watt counts. The pyramidal horn still dominates where linear polarization and maximum directivity are the goals, with a cross-polarization discrimination of about 62 decibels, far beyond the 30-decibel minimum recommended for satellite systems.

The dual-simulator exercise also yielded instructive engineering lessons about the tools themselves. Ansys HFSS, built on the frequency-domain finite element method with an adaptive tetrahedral mesh, consumed roughly 15 gigabytes of memory and delivered the highest accuracy on curved geometries. CST Studio Suite, using the time-domain finite integration technique with a hexahedral mesh, required only about 1.5 gigabytes and produced broadband results in a single run, though its Fourier-transform-based frequency extraction introduced a shift of roughly 1 gigahertz in the location of the reflection coefficient minimum. A gain discrepancy of 1.63 decibels between platforms for the conical horn fell squarely within the sub-2-decibel spread documented in prior comparative studies of the two solvers.

Beyond the immediate results, the study lays deliberate groundwork for what comes next. The smooth-wall conical horn is the direct geometric ancestor of the conical corrugated horn, the gold-standard feed for satellite reflector systems thanks to its symmetric radiation pattern and minimal cross-polarization. The researchers, working within a broader doctoral project, plan to add corrugations to the validated cone, optimize the corrugation depth and pitch to suppress surface currents, and fabricate a prototype for measurement. The present results serve as the reference baseline against which that upgraded design will be judged.

In an era when mega-constellations and flexible geostationary spacecraft are pushing antenna engineering to new heights, there is something almost reassuring about a study that goes back to fundamentals. The horn antenna, first sketched in the late nineteenth century and battle-tested through radar, radio astronomy, and every satellite generation since, still responds beautifully to careful analytical design and rigorous simulation. What this comparison shows is that the choice between pyramid and cone is not about which antenna is better, but about which task you need done, and for the circularly polarized world of satellite communications, the cone remains the shape of the future.

Subject of Research: Comparative electromagnetic design and simulation of pyramidal and conical horn antennas for X-band satellite communication systems

Article Title: Design and electromagnetic analysis of pyramidal and conical horn antenna for X-band satellite communication systems

Article References: Topal, H.-A., & Grigorie, T. L. (2026). Design and electromagnetic analysis of pyramidal and conical horn antenna for X-band satellite communication systems. Frontiers in Antennas and Propagation, 4, Article 1828476. https://doi.org/10.3389/fanpr.2026.1828476

Image Credits: AI Generated

DOI: 10.3389/fanpr.2026.1828476

Keywords: horn antenna, X-band, satellite communication, pyramidal horn, conical horn, circular polarization, waveguide, Ansys HFSS, CST Studio Suite, reflection coefficient, gain, reflector feed

The research team, led by Adnan M. Taha and including Mahdi Ghafourivayghan, Konstantin Burlakov, Sergey Shabunin, and Mohammad Alibakhshikenari, set out to address a persistent bottleneck in computational electromagnetics. Commercial full-wave solvers such as ANSYS HFSS, CST, and FEKO discretize an entire three-dimensional volume into a finite-element mesh, and their cost balloons when reflected waves must be tracked near a boundary. When the antenna operates in its near or intermediate zone, the amplitude and phase of the field cannot be inferred from a simple aperture distribution; every field component must be computed numerically, which dramatically inflates processing time and memory demands. For applications like radar sensors, subsurface radiolocation, and level gauges, where the far-zone condition is simply never met, this is more than an inconvenience.

The core of the new method is the Green’s tensor function, a mathematical object that encodes how an infinitesimal electric or magnetic current source radiates through a specified environment. In unbounded homogeneous space, the Green function takes a comparatively simple form. In a layered medium, however, it must absorb the thickness, number, and electromagnetic parameters of every layer, including permittivity, permeability, and conductivity. The authors build these properties into characteristic functions g(z, z’) and f(z, z’), which solve Sturm-Liouville-type differential equations and automatically satisfy all boundary conditions at each interface. Crucially, the modal conductances are recalculated recursively through the stack using an equivalent transmission-line model, in which spectral components of the field are mapped onto voltages and currents in equivalent circuits. Once this analytical groundwork is laid, the field can be evaluated only where it is actually needed, rather than everywhere in space.

To model a real aperture antenna, the team begins with the Huygens element, a pair of orthogonally crossed electric and magnetic dipoles that together reproduce the radiation of an elementary patch of wavefront. The electric field is obtained by integrating the external electric and magnetic currents over the source region, weighted by the appropriate Green’s tensor components. Because a Huygens element radiates a curved, non-uniform wavefront rather than a plane wave, its reflection from a nearby interface behaves nothing like the textbook plane-wave diffraction problem, and the Green’s-function framework captures this distinction exactly. The formulation also yields closed-form far-zone expressions via the saddle-point method, providing a convenient analytical check: the radial field component vanishes, and the radiation maximum points toward the interface, exactly as physics demands.

The extension from the elementary Huygens source to a practical pyramidal horn is where the study claims its principal advance over the authors’ earlier work. The horn flares in both principal planes, combining the properties of E-plane and H-plane sectoral horns, and its aperture field carries a quadratic phase variation that reflects the true curvature of the wavefront. The researchers derive a rigorous aperture integration in which the path-length difference across the aperture is expanded binomially, and the resulting integrals are evaluated in terms of cosine and sine Fresnel integrals. This captures interference structure near the reflector that a simple Huygens source fundamentally cannot represent, making the tool genuinely design-ready rather than a purely theoretical exercise.

Numerical stability is handled through a documented three-region spectral truncation strategy. The integration domain in wave-number space is split into an evanescent region of exponentially decaying near-field contributions, a narrow singularity gap around the branch point where split-path integration is applied, and a propagating region of oscillatory far-field radiation. Convergence analysis shows the truncation error decays exponentially with the upper limit, achieving one percent accuracy well within the adopted defaults, while the singularity treatment remains stable for gap sizes down to ten to the minus twenty-fifth. A parametric robustness study across horn heights from half a wavelength to two wavelengths, frequencies from 0.5 to 3 gigahertz, and substrate permittivities from 1 to 10 confirms that the chosen settings sit on a stable plateau and need no geometry-specific retuning.

The validation against ANSYS HFSS is the study’s most persuasive evidence. On identical observation grids, the proposed method required 30.9 seconds of wall-clock time against 88 seconds for HFSS, a roughly threefold speed-up, and used 200 megabytes of memory against 749 megabytes, a nearly fourfold reduction. The speed advantage stems from the region-of-interest strategy: the spectral integral is evaluated only at the user-specified observation points, whereas the finite-element solver must discretize the entire computational volume. Error budgets quantify the agreement precisely. The L2-norm relative error for the electric field magnitude is 2.78 percent, with maximum deviation of 2.29 percent, while the phase component shows an L2 error of 4.50 percent, a figure the authors attribute to the notorious sensitivity of phase near field nulls.

Even more telling is how the error scales with antenna height above the interface. At a separation of half a wavelength, deep in the reactive near field, the L2 error against HFSS is about 2.6 to 2.9 percent. At three-quarters of a wavelength it drops to roughly 0.65 percent, and at one and a half wavelengths it falls below 0.01 percent as the observation domain moves into the Fresnel region. Notably, the error shows only weak dependence on frequency and substrate permittivity, with higher permittivity actually marginally reducing the error at close separations because stronger field confinement diminishes the relative weight of the evanescent spectral tail. For radar-sensor and level-gauge designers, these numbers suggest the method can be trusted across a decade of bandwidth without recalibration.

The comparison also exposed an interesting divergence between the two approaches at a perfect electric conductor boundary, where the Green’s-function method delivered cleaner wave patterns than the finite-element reference. The authors point out that HFSS results depend on mesh symmetry and on the correct selection of the bounding box around the analyzed object; an asymmetric mesh around a structure symmetric with respect to the reference plane can introduce spurious field asymmetry. The analytical method, by contrast, is electrodynamically exact and automatically enforces all boundary conditions, eliminating such numerical artifacts. In benchmark runs over a dielectric boundary, the conventional solver took roughly twice as long at a comparable spatial step.

The authors are careful to delineate the method’s limits. Its computational advantage is specific to planar, stratified reflecting surfaces; for finite-sized, curved, or laterally inhomogeneous reflectors, edge diffraction and geometric scattering fall outside the stratified-media kernel, and full-wave solvers remain the appropriate tools. Substrates containing vias, patches, or etched patterns would require augmenting the transmission-line recursion with periodic or moment-method treatments. Within its domain, however, the framework offers a unified and efficient foundation that extends naturally to printed and slot antennas, transmitarrays, and reflectarrays, whose multiple functional layers are handled natively by stratified-media Green’s functions. As near-field applications multiply, from high-resolution electromagnetic imaging and secure short-range communication to over-the-air testing of 5G and 6G arrays, tools that trade brute-force meshing for analytical rigor are likely to become indispensable to the antenna community.

Subject of Research: Electromagnetic near-field analysis of pyramidal horn antennas above layered reflecting media using dyadic Green's functions

Article Title: Analysis of pyramidal horn antennas near a reflecting surface using Green’s functions

Article References: Taha, A. M., Ghafourivayghan, M., Burlakov, K., Shabunin, S., & Alibakhshikenari, M. (2026). Analysis of pyramidal horn antennas near a reflecting surface using Green’s functions. Results in Engineering, 32, Article 113033. https://doi.org/10.1016/j.rineng.2026.113033

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113033

Keywords: pyramidal horn antenna, Green's functions, near-field, reflecting surface, stratified media, ANSYS HFSS, electromagnetic modeling, radar sensors, spectral integration, computational electromagnetics, 5G, aperture antennas